#16374: better two_squares, three_squares, four_squares for small input
-------------------------------------+-------------------------------------
Reporter: vdelecroix | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.3
Component: number theory | Resolution:
Keywords: | Merged in:
Authors: Vincent Delecroix | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/vdelecroix/16374 | 17883e34f96f7f78f35f56bad527dcbaa728169d
Dependencies: | Stopgaps:
-------------------------------------+-------------------------------------
Comment (by vdelecroix):
Replying to [comment:25 leif]:
> Replying to [comment:24 vdelecroix]:
> > Just to mention: if there is an overflow, the error is very explicit
> > {{{
> > sage: from sage.rings.sum_of_squares import two_squares_pyx
> > sage: two_squares_pyx(2**65+19)
> > Traceback (most recent call last):
> > ...
> > OverflowError: long int too large to convert
> > }}}
>
> I rather meant overflows in the C/Cython code, where just modulo
arithmetic happens, without throwing exceptions. (With using `unsigned
long`s you're probably on the safe[r] side, but that's something I(?)'ll
have to check more carefully...)
There are only two places were overflow may occur:
- the input
- when we rely on long double to perform the square root (i.e. are we
sure that an `unsigned long` fits into a `long double` ?)
All integers that appear inside the function are smaller than the input.
So, no trouble here.
Vincent
--
Ticket URL: <http://trac.sagemath.org/ticket/16374#comment:27>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
